If you take a picture in a room with all the lights off, would you be able to edit the picture later to see it like you would with lights on??
For all practical purposes: No.
Photography is the recording of light. In the total absence of light there is nothing for a camera to record except the random noise generated by the camera itself.
There are a few possible edge cases where one might be able to describe a room with all of the lights off and still be able to record something with a camera.
It all kind of depends on how dark the room is with, as the question states it:
"... all of the lights off."
If there is any light illuminating the room from light sources outside the room so that the room is only very dark but not totally dark, then that light, properly recorded, can reveal at least some things about what the room looks like. If the image is mildly underexposed but recorded with the raw data from the sensor preserved one could conceivably develop the raw image to be much brighter and reveal details about the room.
Even then it will not look like the room would look with "lights on" because those lights would almost certainly be illuminating the room from different directions and angles at different light ratios than the light spilling over into the room from somewhere else.
It could also depend upon what one means when one says, "light."
Visible light is so-called because it is the range of the light spectrum that causes a chemical response in the human retina. There are also ranges of light above and below the visible spectrum that can be recorded by certain types of cameras. Infrared light, which humans do not perceive with their eyes, can be recorded by a camera sensitive to infrared. At the other end of the visible spectrum, cameras sensitive to UV light can record the UV wavelengths that our eyes do not perceive. In the case of a room, unless it is at absolutely 0 Kelvin (absolute zero, where molecular motion ceases), then the objects in the room that are at slightly different temperatures from one another could be distinguished. This is how many "night vision" goggles and security cameras work - they are sensitive to infrared light.
That depends a lot on how you take the picture originally. If you properly expose it by using a sufficiently long shutter speed for the aperture and ISO in use, then you could probably get something that approximates what the room looks like with the lights on. But there would be significant differences, still - anything that moved during the long exposure would be at least blurred, if not completely gone if it moved fast enough; there's a lot of detail and subtlety to inter-object reflections that would be completely different in a low-light situation; noise levels can be significantly affected by long exposures as well, although that varies significantly depending on whether you're talking film or digital; and probably several others... But if all you want is an image that's not totally black, then, yes, that is achievable...